The credit of carrying Jainism in South India is given to Bhadrabahu. It is important to understand the role of each option mentioned in the question to have a better understanding.
Option 1: Sudharmana - There is no significant historical evidence to suggest that Sudharmana played a major role in carrying Jainism in South India.
Option 2: Indrabhuti - Indrabhuti is associated with the establishment of the Pashupata Shaivism sect in ancient India and not with Jainism.
Option 3: Bhadrabahu - Bhadrabahu is credited with carrying Jainism to South India. He was a revered Jain sage and scholar who migrated from Magadha region to Karnataka during the time of Emperor Chandragupta Maurya.
Option 4: Sthulabhadra - Sthulabhadra was a Jain scholar during the time of Mahavira, but there is no historical evidence to suggest that he played a significant role in carrying Jainism in South India.
In conclusion, option 3, Bhadrabahu, is the correct answer as he is attributed with carrying Jainism to South India.